This is a pretty odd take. Believing anything is optional. You may believe that the evidence is incontrovertible, but even that is an optional belief. The person you're responding to is just signaling that the questions are not based on climate change skepticism. In 100 years that signal may no longer be valuable, but today it probably is.
Everything can be wrong. Even theory of gravitation. That’s besides the point.
Except nothing.
> hard scientific facts that have been proven experimentally
Science isn't in the business of proving things. Science develops explanatory models that account for known evidence. Saying that science proves anything is super wrong and leads to all kinds of problems.
I want to emphasize my point again - we have 2 arguments. Argument A and argument B. A is presenting scientific evidence, in your corrected terms - presenting a model of climate change. Argument B is anecdotal evidence. The fact that they are both argued on the same stage gives the audience (who may not know anything about A or B) a false assurance that both A and B are arguable and therefore, they are on the stage. It is fine for casual conversations, I am speaking about large debates that we still fucking have about whether Earth is flat. It is equivalent of "Trolling" and should not be entertained.
I think what people who get rankled by this have in mind is a certain, pluralistic connotation of "believe." Often when someone says, "I believe in Christianity," it's implied that atheists or people of other faiths are not unreasonable to believe differently. (Something similar could be said about political or ethical beliefs. It's difficult to spell out the sense in which you can view someone who disagrees with you as reasonable, but I think you know what I mean.) So people who think "belief" is not applicable to global warming or evolution are trying to deny that we should be pluralistic about these matters.
I still think this is a somewhat obtuse equivocation on the word "belief," but I think I understand the intuition beneath it.